Distance changing at rate of 3.94 inches/sec.
Given,
In the question:
The wall is decreasing at a rate of 9 inches per second.
and this distance is currently 61 inches.
The ladder is 152 inches long.
To find out how fast is the distance changing
Now, According to the question:
we know that
h² + b² = L² …1
h² + b² = 152²
Apply here derivative w.r.t. time
2h dh/dt + 2b db/dt = 0
h dh/dt + b db/dt = 0
db/dt = - h/b × dh/dt ….2
Height of distance is currently = 61 inches
Substitute the values
h² + b² = L²
61² + b² = 152²
b² = 19383
b = 139.223
and ,we know dh/dt = -9 inch/sec
From equation 2
db/dt = -61/139.223 (-9)
db/dt = 3.94 inches/sec
Hence, Distance changing at rate of 3.94 inches/sec.
Learn more about Distance at:
brainly.com/question/15256256
#SPJ4
